I managed to get one of it's many ticks off, but since we are going to the rescue center anyway, I wasn't sure it was worth stressing it out further just for 1 fewer day with a couple fewer ticks.

Woman on the phone said give it some scrambled egg, and it had some.
Gave it expensive all-meat cat food, had a lot of that.
Taking it to the rescue in the morning to get her looked after.

Lovely little beast, I hope they can look after her well. I'll stay in touch with them anyway.